avirup2018 wrote:
lacktutor wrote:
Is x an odd number??
(Statement1) 1< x < 8
x could be odd or even number in the range from 1 to 8.
Insufficient
(Statement2):
\(7x^{2}\) has four positive number factors
If the value of x is equal to 7, statement2 will have 4 positive factors
—> x=7 —> \(7*7^{2}= 7^{3}\)
(3+1)= 4 ( 1, 7,49, 343)
—> x is odd (YES)
If \(x= 3^{1/2}\), then 7*3 has also 4 positive factors (—> 1,3,7,21)
x is not odd ( NO)
Insufficient
Taken together 1&2,
—> x could be \(3^{1/2}\) or 7 in the range from 1 to 8.
Insufficient
The answer is E
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Can you please guide how to think of the Exception like you have thought of 3^(1/2) a the value of x here.... how did you choose amonst so many values....Please guide
Hi,
avirup2018Firstly, nothing tells us whether x is integer or not in the question stem. Well, we need to check non-integer values of x too.
Secondly, statement2 says there are 4 factors of \(7x^{2}\).
—> there are two cases of finding factors (formula)
Case1: (1+1)(1+1) = 4
\(7x^{2}\) => \(7^{1}\)— Ok. \(x^{2}\) should be equal to any prime number except 7.
—> \(x^{2}= 5\) —> \(x= 5^{1/2}\)
—> \(7x^{2} = 7^{1}*5^{1}\) —> (1+1)(1+1) = 4 ( x is not an integer)
Case2: 3+1= 4
\(7x^{2}\) = should be equal to \(7^{3}\)
—> x= 7 (x is an integer)